/* -------------------------------------------------------------- */ /* (C)Copyright 2006,2007, */ /* International Business Machines Corporation */ /* All Rights Reserved. */ /* */ /* Redistribution and use in source and binary forms, with or */ /* without modification, are permitted provided that the */ /* following conditions are met: */ /* */ /* - Redistributions of source code must retain the above copyright*/ /* notice, this list of conditions and the following disclaimer. */ /* */ /* - Redistributions in binary form must reproduce the above */ /* copyright notice, this list of conditions and the following */ /* disclaimer in the documentation and/or other materials */ /* provided with the distribution. */ /* */ /* - Neither the name of IBM Corporation nor the names of its */ /* contributors may be used to endorse or promote products */ /* derived from this software without specific prior written */ /* permission. */ /* Redistributions of source code must retain the above copyright */ /* notice, this list of conditions and the following disclaimer. */ /* */ /* Redistributions in binary form must reproduce the above */ /* copyright notice, this list of conditions and the following */ /* disclaimer in the documentation and/or other materials */ /* provided with the distribution. */ /* */ /* Neither the name of IBM Corporation nor the names of its */ /* contributors may be used to endorse or promote products */ /* derived from this software without specific prior written */ /* permission. */ /* */ /* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */ /* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */ /* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */ /* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */ /* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */ /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */ /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */ /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */ /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */ /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */ /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */ /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */ /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* -------------------------------------------------------------- */ /* PROLOG END TAG zYx */ #ifdef __SPU__ #ifndef _LGAMMAF4_H_ #define _LGAMMAF4_H_ 1 #include #include "lgammad2.h" #include "recipf4.h" #include "logf4.h" #include "sinf4.h" #include "truncf4.h" /* * FUNCTION * vector float _lgammaf4(vector float x) - Natural Log of Gamma Function * * DESCRIPTION * _lgammaf4 calculates the natural logarithm of the absolute value of the gamma * function for the corresponding elements of the input vector. * * C99 Special Cases: * lgamma(0) returns +infinite * lgamma(1) returns +0 * lgamma(2) returns +0 * lgamma(negative integer) returns +infinite * lgamma(+infinite) returns +infinite * lgamma(-infinite) returns +infinite * * Other Cases: * lgamma(Nan) returns Nan * lgamma(Denorm) treated as lgamma(0) and returns +infinite * */ static __inline vector float _lgammaf4(vector float x) { vec_float4 inff = (vec_float4)spu_splats(0x7F800000); vec_float4 zerof = spu_splats(0.0f); vec_float4 pi = spu_splats((float)PI); vec_float4 sign_maskf = spu_splats(-0.0f); vector unsigned int gt0; /* This is where we switch from near zero approx. */ vec_float4 mac_switch = spu_splats(0.16f); vec_float4 shift_switch = spu_splats(6.0f); vec_float4 inv_x, inv_xsqu; vec_float4 xtrunc, xstirling; vec_float4 sum, xabs; vec_uint4 isnaninf, isshifted; vec_float4 result, stresult, shresult, mresult, nresult; /* Force Denorms to 0 */ x = spu_add(x, zerof); xabs = spu_andc(x, sign_maskf); gt0 = spu_cmpgt(x, zerof); xtrunc = _truncf4(x); /* * For 0 < x <= 0.16. * Approximation Near Zero * * Use Maclaurin Expansion of lgamma() * * lgamma(z) = -ln(z) - z * EulerMascheroni + Sum[(-1)^n * z^n * Zeta(n)/n] */ mresult = spu_madd(xabs, spu_splats((float)ZETA_06_DIV_06), spu_splats((float)ZETA_05_DIV_05)); mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_04_DIV_04)); mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_03_DIV_03)); mresult = spu_madd(xabs, mresult, spu_splats((float)ZETA_02_DIV_02)); mresult = spu_mul(xabs, spu_mul(xabs, mresult)); mresult = spu_sub(mresult, spu_add(_logf4(xabs), spu_mul(xabs, spu_splats((float)EULER_MASCHERONI)))); /* * For 0.16 < x <= 6.0, we are going to push value * out to an area where Stirling's approximation is * accurate. Let's use a constant of 6. * * Use the recurrence relation: * lgamma(x + 1) = ln(x) + lgamma(x) * * Note that we shift x here, before Stirling's calculation, * then after Stirling's, we adjust the result. * */ isshifted = spu_cmpgt(shift_switch, x); xstirling = spu_sel(xabs, spu_add(xabs, spu_splats(6.0f)), isshifted); inv_x = _recipf4(xstirling); inv_xsqu = spu_mul(inv_x, inv_x); /* * For 6.0 < x < infinite * * Use Stirling's Series. * * 1 1 1 1 1 * lgamma(x) = --- ln (2*pi) + (z - ---) ln(x) - x + --- - ----- + ------ ... * 2 2 12x 360x^3 1260x^5 * * */ sum = spu_madd(inv_xsqu, spu_splats((float)STIRLING_10), spu_splats((float)STIRLING_09)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_08)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_07)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_06)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_05)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_04)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_03)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_02)); sum = spu_madd(sum, inv_xsqu, spu_splats((float)STIRLING_01)); sum = spu_mul(sum, inv_x); stresult = spu_madd(spu_sub(xstirling, spu_splats(0.5f)), _logf4(xstirling), spu_splats((float)HALFLOG2PI)); stresult = spu_sub(stresult, xstirling); stresult = spu_add(stresult, sum); /* * Adjust result if we shifted x into Stirling range. * * lgamma(x) = lgamma(x + n) - ln(x(x+1)(x+2)...(x+n-1) * */ shresult = spu_mul(xabs, spu_add(xabs, spu_splats(1.0f))); shresult = spu_mul(shresult, spu_add(xabs, spu_splats(2.0f))); shresult = spu_mul(shresult, spu_add(xabs, spu_splats(3.0f))); shresult = spu_mul(shresult, spu_add(xabs, spu_splats(4.0f))); shresult = spu_mul(shresult, spu_add(xabs, spu_splats(5.0f))); shresult = _logf4(shresult); shresult = spu_sub(stresult, shresult); stresult = spu_sel(stresult, shresult, isshifted); /* * Select either Maclaurin or Stirling result before Negative X calc. */ vec_uint4 useStirlings = spu_cmpgt(xabs, mac_switch); result = spu_sel(mresult, stresult, useStirlings); /* * Approximation for Negative X * * Use reflection relation: * * gamma(x) * gamma(-x) = -pi/(x sin(pi x)) * * lgamma(x) = log(pi/(-x sin(pi x))) - lgamma(-x) * */ nresult = spu_mul(x, _sinf4(spu_mul(x, pi))); nresult = spu_andc(nresult, sign_maskf); nresult = spu_sub(_logf4(pi), spu_add(result, _logf4(nresult))); /* * Select between the negative or positive x approximations. */ result = spu_sel(nresult, result, gt0); /* * Finally, special cases/errors. */ /* * x = non-positive integer, return infinity. */ result = spu_sel(result, inff, spu_andc(spu_cmpeq(x, xtrunc), gt0)); /* x = +/- infinite or nan, return |x| */ isnaninf = spu_cmpgt((vec_uint4)xabs, 0x7FEFFFFF); result = spu_sel(result, xabs, isnaninf); return result; } #endif /* _LGAMMAF4_H_ */ #endif /* __SPU__ */